Question: $\dfrac{5}{2} \div \dfrac{5}{7} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{5}{7}$ is $\dfrac{7}{5}$. Therefore: $ \dfrac{5}{2} \div \dfrac{5}{7} = \dfrac{5}{2} \times \dfrac{7}{5} $ $ \phantom{\dfrac{5}{2} \times \dfrac{7}{5}} = \dfrac{5 \times 7}{2 \times 5} $ $ \phantom{\dfrac{5}{2} \times \dfrac{7}{5}} = \dfrac{35}{10} $ $ \phantom{\dfrac{5}{2} \times \dfrac{7}{5}} = \dfrac{7}{2} $